Square and Cube Roots Quiz Set 009

It is not possible for the square of any number to end in 2, 3, 7 or 8. Hence the answer is 0.

We know that 0.03 = $√0.0009$, so by inspection we can see that 0.0509 - 0.05 will give us 0.0009.

By inspection, we can easily see that the formula (a - b) × (a + b) can be used to simplify like this: $√{(11)^2 - (2√3)^2}$, which is same as $√{121 - (2^2 × 3)}$, which is same as $√{121 - 12}$ = $√109$.

The given expression can be simplified to ${{(√2)^2} - 5 × 4}/{5 × √2}$, which is same as ${2 - 20}/{5 × √2}$, which is same as ${-18/{5 × √2}$. Rationalizing, we get ${-18/{5 × √2} × {√2/√2}$ which gives ${-18√2}/10$ which = -2.546.

We can see that 0.09 × 0.09 × 0.09 = 0.000729, so cube root is 0.09.